Gaussian Process Quantile Regression using Expectation Propagation
This work provides a probabilistic framework for quantile regression, which is incremental as it builds on existing methods with a new computational approach.
The authors tackled quantile regression by developing a Gaussian process model that minimizes the expected tilted loss function, using Expectation Propagation for efficient learning. The method was shown to be competitive with state-of-the-art approaches on synthetic and real datasets.
Direct quantile regression involves estimating a given quantile of a response variable as a function of input variables. We present a new framework for direct quantile regression where a Gaussian process model is learned, minimising the expected tilted loss function. The integration required in learning is not analytically tractable so to speed up the learning we employ the Expectation Propagation algorithm. We describe how this work relates to other quantile regression methods and apply the method on both synthetic and real data sets. The method is shown to be competitive with state of the art methods whilst allowing for the leverage of the full Gaussian process probabilistic framework.